Bistable Structures Research Articles

Experimental study on broadband bistable energy harvester with L-shaped piezoelectric cantilever beam

This paper presents an experimental study of the broadband energy harvesting and dynamic responses of an L-shaped piezoelectric cantilever beam. Experimental results show that the L-shaped piezoelectric beam generates two optimal voltage peaks when the horizontal beam size is similar to the vertical beam size. Several optimized L-shaped piezoelectric cantilever beam structures are proposed. Power generation using the inverted bistable L-shaped beam is better. It is observed experimentally that the inverted bistable L-shaped beam structure shows obvious bistable characteristics and hard spring characteristics. Furthermore, the corresponding relationship between the bistable phase portrait and the potential energy curve is found in the experiment. This is the first time that a phase portrait for stiffness hardening of an L-shaped beam has been found experimentally. These results can be applied to analysis of new piezoelectric power generation structures.

Pore opening and breathing transitions in metal-organic frameworks: Coupling adsorption and deformation

Soft porous crystals undergo large structural transformations under a variety of physical stimuli. Breathing-like transformations, occurring with a large volume change, have been associated with an existence of bi-stable or multi-stable crystal structures. Understanding of the mechanism of these transformations is essential for their potential applications in gas adsorption, separation and storage. However, the generic description is still missing. Here, we provide a detailed, multiscale qualitative and quantitative analysis of the adsorption-induced “breathing” transformations in two metal organic frameworks (MOFs): MIL-53(Al) which is a reference case of our approach, and recently synthesized JUK-8, which does not show any bistability without adsorbate. The proposed approach is based on atomistic simulations and does not require any empirical or adjustable parameters. It allows for a prediction of potential structural transformations in MOFs including the adsorption induced deformations derived from adsorption stress model. We also show that the quantitative agreement between calculated and experimental results critically depends on the quality of the dispersion energy correction. Our methodology represents a new, powerful tool for designing and screening of flexible materials, alternative and complimentary to experimental approaches.

Field-triggered vertical positional transition of a microparticle suspended in a nematic liquid crystal cell.

In this paper, based on the numerical calculation of total energy utilizing the Green's function method, we investigate how a field-triggered vertical positional transition of a microparticle suspended in a nematic liquid crystal cell is influenced by the direction of the applied field, surface anchoring feature, and nematic's dielectric properties. The new equilibrium position of the translational movement is decided via a competition between the buoyant force and the effective force built on the microparticle by the elastic energy gradient along the vertical direction. The threshold value of external field depends on thickness L and Frank elastic constant K and slightly on the microparticle size and density, in a Fréedericksz-like manner, but by a factor. For a nematic liquid crystal cell with planar surface alignment, a bistable equilibrium structure for the transition is found when the direction of the applied electric field is (a) perpendicular to the two plates of the cell with positive molecular dielectric anisotropy or (b) parallel to the two plates and the anchoring direction of the cell with negative molecular dielectric anisotropy. When the electric field applied is parallel to both plates and perpendicular to the anchoring direction, the microparticle suspended in the nematic liquid crystal tends to be trapped in the midplane, regardless of the sign of the molecular dielectric anisotropy. Such a phenomenon also occurs for negative molecular dielectric anisotropy if the external field is applied perpendicular to the two plates. Explicit formulas proposed for the critical electric field agree extremely well with the numerical calculation.

A novel solar tracking model integrated with bistable composite structures and bimetallic strips

Solar tracking model has attracted substantial academic and industrial interests owing to its high efficiency of solar panels. However, the complexity of the structure by using the mechanical structure is also increased. This paper proposes a novel solar tracking model that is composed of bistable laminates, Ni36/Mn75Ni15Cu10 bimetallic strip and organic solar cell. The bistable structure can serve as the steering mechanism and consequently reduces the number of needed parts. With the sunshine, the bimetallic strip will bend and deform due to the influence of temperature depending on the shadow area. The bending motion of Ni36/Mn75Ni15Cu10 bimetallic strip drives the bistable laminates structure snapping from one stable configuration to another, which process is reversible. The change of bistable laminates shape holds the solar cell perpendicular to light to receive the maximum solar energy. Experimental results demonstrate that the deformation process of this solar tracking model is feasible. This novel solar tracking model can be extensively used in engineering fields, due to the use of bistable laminates, the weight of the solar tracker has been greatly reduced.

Snap-Through Buckling Mechanism for Frequency-up Conversion in Piezoelectric Energy Harvesting

This paper describes a piezoelectric energy harvester employing a snap-through buckling (STB) mechanism for frequency-up conversion (FuC). The harvester consists of two main components: a bistable mechanical structure and one piezoelectric cantilever beam. The device is designed by means of analytical methods and numerical simulations. A proof-of-concept prototype is manufactured and tested under low frequency mechanical excitation. Experimental results show that, if the STB is induced, from the second stable configuration back to the undeformed one, the FuC is obtained and the response of the beam presents frequency components in a wide range, even though the resonant frequency of the cantilever beam is not excited. The results are hence in agreement with the expected behavior: if the device, forced in the second stable configuration, is subject to a low-frequency excitation whose amplitude exceeds a threshold, STB is triggered and the ensuing FuC provokes a widening of the beam vibrations frequency range and consequently a significant effectiveness in terms of power output. A maximum power of 4 mW is obtained by using an optimal resistive load as STB from a stable configuration of the bistable mechanism to the other one is triggered; a maximum energy of 4.5 μ J is obtained in case of a rectifier circuit with storage capacitor.

Analysis of electrophysical characteristics of bistable MIS structures with samarium and cerium fluorides

Analysis of electrophysical characteristics of bistable MIS structures with samarium and cerium fluorides

Multi-objective optimisation of deployable bistable scissor structures

Lightweight bistable deployable structures can be designed to be transportable and reusable. They instantaneously achieve some structural stability when transformed from the compact to the deployed state through a controlled snap-through, as a result of intended geometric incompatibilities between the beams. Due to their transformable bistable nature their design requires assessing both their non-linear transformation behaviour, as well as their service state in the deployed configuration. The requirement of a low peak force during transformation can be shown to oppose the high stiffness requirement in the deployed state; their design can therefore be formulated as a multi-objective non-linear optimisation problem. In this contribution, a size and shape optimisation method is elaborated by choosing the best material combinations, the optimal geometry of the structure and beam cross-sections. The originality of this contribution is the use of a multi-objective evolutionary algorithm to structurally optimise bistable scissor structures taking into account the deployed state as well as the transformation phase. First, the method is applied to optimise a single bistable scissor module. Next, a multi-module bistable scissor structure is optimised and the single module and full structure based approaches are critically compared.

Bistable structures with controllable wrinkled surface

The deformation of a tri-layer composite rubber from a mono-stable saddle, a monostable state with wrinkles, a bistable cylinder, to a bistable state with wrinkles was investigated in this work. Among these forms, the wrinkled bi-stability was a unique shape that combined two different deformations into one structure and was primarily studied. The dependence of the rubber shape on the geometric and mechanical parameters was investigated. The phase diagram for the rubber transformation provides accurate pre-strain values and width of structure that correspond to various states. Finite element analysis could reproduce these deformation states well considering the above influencing factors. For the bistable surface, the inner layer was wrinkled, while the outer layer remained flat at the same pre-strain. The morphological differences could be related to the constraints in a manner that is analogous to unidirectional strain. Furthermore, the pre-strain field of the top and bottom layers could be simplified to one layer using Poisson’s ratio. The investigated deformation processes have potential applications for the precise control of flexible machines and robots.

Suppression of Cross-Well Oscillations for Bistable Composites Through Potential Well Elimination

Abstract Although there have been numerous efforts into harnessing the snap through dynamics of bistable structures with piezoelectric transducers to achieve large energy conversion, these same dynamics are undesirable under morphing applications where stationary control of the structure’s configuration is paramount. To suppress cross-well vibrations that primarily result from periodic excitation at low frequencies, a novel control strategy is proposed and implemented on the piezoelectrically generated bistable laminate, which consists of only macro fiber composites (MFCs) in a [0MFC/90MFC]T layup. While under cross-well regimes such as subharmonic, chaotic, or limit cycle oscillations, a single MFC is actuated to the laminate’s limit voltage to eliminate one of its potential wells and force it into the remaining stable state. Simultaneously, a positive position feedback (PPF) controller suppresses the resulting single-well oscillations through the other MFC. This dual control strategy is numerically and experimentally demonstrated through the suppression of various cross-well regimes and results in significant reduction of amplitude. The active control capability of the laminate prevents snap through instability when under large enough external vibrations.

Plant‐Inspired Soft Bistable Structures Based on Hygroscopic Electrospun Nanofibers

AbstractThe tissue composition and microstructures of plants have dynamic morphologies that change according to their environments. Recently, multifunctional responsive materials and smart structures also took inspiration from these plants' features.Dionaea muscipulaleaves provide a remarkable example of an optimized structure that, owing to the synergistic integration of bistability, material, and geometrical properties, permits to overcome the performance limits of purely diffusive processes. In this paper, a hygroscopic bistable structure (HBS) inspired by the Venus flytrap leaves is presented, obtained by bonding prestretched poly(dimethylsiloxane) (PDMS) layers prior to depositing electrospun polyethylene oxide (PEO) nanofibers. A hygroresponsive bilayer (HBL) is also obtained by electrospinning of PEO on an unstretched PDMS layer. The hygroscopic material (Young's modulus and hygroscopic expansion) is mechanically characterized so as to predict the response time of a bending HBL in response to a step humidity variation. The HBS response time (≈1 s) is sensibly lower than the one of purely diffusive HBL (≈10 s) thanks to bistability. An illustrative implementation is also presented, exploiting an HBS to trigger the curvature of a PDMS optical focusing system. The developed plant‐inspired soft bistable structure can also be used for sensing (e.g., humidity), energy harvesting, as well as advanced soft robotics applications.

1/2 sub-harmonic resonance in bistable structure and its effect on vibration isolation characteristics

<sec>In the extensive modern applications, the low-frequency and heavy-load isolators are needed to reduce the vibration transmissions. The unique properties of nonlinear systems, such as jumping, bifurcation and chaos, provide new ideas for designing the new functional structures. Bistable system is a typical non-linear system, features highly static and low dynamic stiffness, which promises to realize a low-frequency isolator with ensuring heavy load capacity. However, more studies are necessary to clarify the sub-harmonic resonance and its generation process, parameter influences, vibration isolation characteristics of the bistable structure.</sec><sec>By adopting the equivalent, analytical, numerical and experimental methods, we study the 1/2 sub-harmonic resonance, evolution process and its influence on the vibration isolation characteristics of the bistable structure in this paper. When the amplitude or nonlinear stiffness coefficient <i>k</i><sub>n</sub> increases to a certain extent, 1/2 sub-harmonic resonance appears, where the response contains high-amplitude <i>ω</i>/2 component under the excitation frequency <i>ω</i>, so the energy is transferred from high frequency to low frequency. We study the bifurcation and varying processes of the fundamental and 1/2 sub-harmonic transmission by increasing the amplitude. At critical bifurcation amplitude, the sub-harmonic transmission rapidly increases from 0 to a large peak value. And then, it decreases gradually when the damping is absent. However, the peak value of 1/2 sub-harmonic does not cause the fundamental transmission to change suddenly. When considerable damping appears with the increase of the amplitude, 1/2 sub-harmonic does not always exist, instead, it follows an interesting “generation-enhancement-degeneration-disappearance” process. This process possesses great significance in applying the 1/2 sub-harmonic to vibration manipulation or avoiding the resonant enhancement induced by it. </sec><sec>Moreover, in this process, both the peak frequency and the peak transmission of the bistable isolation system descend first. The optimal combination of the parameters can reduce the resonance frequency by 17.8% through increasing the driving amplitude. However, they jump to large values when 1/2 sub-harmonic plays a dominant role. </sec><sec>Additionally, the negative stiffness <i>k</i><sub>0</sub> has a significant effect on the primary resonance characteristics: as |<i>k</i><sub>0</sub>| increases under a specified excitation amplitude, the resonance peak shifts toward higher frequency and the transmission increases. Besides the main effect on the sub-harmonic resonance and the equilibrium point, the nonlinear coefficient <i>k</i><sub>n</sub> also affects the peak and resonance frequency of the system, but the effect is much less than the influence caused by <i>k</i><sub>0</sub>.</sec><sec>Furthermore, the sub-harmonic resonances, bifurcations and vibration isolation characteristics of the bistable bulking beam structure are demonstrated experimentally. The experimental results show that: 1) the 1/2 sub-harmonic resonance can appear in a certain bandwidth and it is not monochromic; 2) the increase of the driving amplitude can reduce the transmission of the fundamental wave; 3) the transmission of 1/2 sub-harmonic jumps from 0 upward to a large value at a critical amplitude, and then it decreases gradually. The experimental results are consistent with the analytical and numerical results. The experiment also demonstrates the law of frequency shifting and the transmission reduction of peak values. Therefore, the appropriate increase of the amplitude can improve the vibration isolation capacity. However, sub-harmonic resonance will reduce the isolation effect. In practical engineering, the strong sub-harmonic resonance should be avoided in a nonlinear vibration isolation system.</sec>

Development of an Interposer with Frequency Conversion Function Using Bistable Structure for a Vibration Energy Harvester

Development of an Interposer with Frequency Conversion Function Using Bistable Structure for a Vibration Energy Harvester

Stress relaxation in asymmetric bistable composites: Experiments and simulations

In the last years, bistable composite structures are finding interest in several aeronautical applications such as power harvesting devices or morphing applications on very small aircraft/drones, not needing servo-activated control systems. Residual stresses, developed upon cooling after curing, leads to warped the composite laminates. Several batches of unsymmetrical and unbalanced [0°/90°] laminates were cured in an autoclave according to a standard temperature cycle, following the pre-preg supplier suggested curing cycle. In order to increase the thermal stresses (and hence the bistability phenomenon), these laminates were removed from the autoclave immediately after the curing reaction and rapidly cooled down at room temperature not applying the indicated cool rate between 2 and 5 °C min−1. During storage at room temperature, thermal stresses changed over time, indicating that asymptotic stress relaxation occurs. The first part of this work looks at residual stress characterization of bistable composite plates measuring the changes of shape observed during room temperature annealing. Rectangular plates were produced and the bistable geometric shapes were accurately assessed using a laser scanner system over several days, in order to monitor the curvature changes due to stress relaxation. Then phenomenological viscoelastic predicting models were proposed for a quick estimate for the strain/stress relaxation phenomenon. The loss of bistability was demonstrated with the help of numerical simulation and experimental testing. The final goal was to gain a better knowledge of the relation between processing and final shape of bistable laminates, in order to make them suitable for application on small air vehicles.

Geometric method to design bistable and non - bistable deployable structures of straight scissors based on the convergence surface

Since Leonardo Da Vinci designed the first deployable structure with scissors some centuries ago, many authors have tried to improve its designs using new geometries. However, these strategies to make deployable structures have limits because they can only be applied in some geometries and the level of the resolution obtained is limited. In this paper a new geometric method to design bistable and non – bistable deployable structures with straight scissors is going to be developed. Using this method, the only limit in the design of deployable structures with straight scissors is the designer's imagination, for example, with this method the designer will be able to design as deployable the Sydney Opera House or a common building with pillars, etc. Consequently, this method is not based on load or forces that can be applied in the structure. An application example is the figure attached in this Abstract where the reader can see the Manantiales Restaurant in Xochimilco designed with straight scissors and without any geometric incompatibility.

On the Nonlinear Snap-Through of Arch-Shaped Clamped–Clamped Bistable Beams

Abstract Bistable compliant elements offer excellent advantages in many applications ranging from high precision sensing to energy harvesting. The essential nonlinear mechanics of such elements are strongly coupled with their buckling mode, geometric parameters, and loading conditions. The force–displacement plot of bistable curved beams could contain a displacement limit point, which cannot be well modeled by the commonly used smooth cubic function and would cause operational problems due to incorrect predictions of the bistability. In this technical brief, the nonlinear bistable mechanics of a compliant curved beam with both ends fixed is analyzed based on the large deflection finite element theory. By using the multistep displacement loading method, the deformation behaviors and their transition from symmetric to asymmetric modes are numerically studied, which provides insights into the force–displacement curve and the multiple snapping pathways. Furthermore, the influences of the structure parameters on bistable mechanics are analyzed, and a quality factor for identifying the occurrence of displacement limit points is introduced for different loading conditions. Finally, a method for achieving a single smooth snapping pathway is proposed, providing a theoretical basis to the design and control of the bistable compliant structures.

Magnetoelastic Metamaterials for Energy Dissipation and Wave Filtering

A novel magnetoelastic mechanical metamaterial consisting of a hyperelastic 2D lattice incorporating permanent magnets is presented and characterized. When properly designed and fabricated, the metamaterial possesses two stable equilibrium configurations (henceforth referred to as hexagonal/hourglass and kagome), both stretching dominated (and hence stiff). The two configurations have significantly different elastic properties and wave propagation characteristics, as shown numerically and experimentally. By switching between the two configurations via uniaxial loading cycles, the material displays hysteresis, thus dissipating substantial amounts of energy; in contrast with purely mechanical bistable structures (e.g., arches, hinged beams and buckled beams), the proposed magnetoelastic metamaterial does not require multiple unit cells in series or stiff boundary conditions to exhibit energy dissipation, thus enabling the implementation of compact stiff dampers. The presence of a bandgap in the kagome configuration (but not in the hexagonal/hourglass configuration) is attributed to an internal resonance mechanism and provides the foundation for the development of compact dynamic filters for mechanical signals.

Tunable bistability of a clamped elastic beam

Bistable structures featuring two stable shapes are commonplace in natural and engineered systems. They can quickly snap from one stable state to the other in response to certain external stimuli, and so have found a range of applications in microswitches, actuators, energy harvesters, and mechanical metamaterials. Buckled beams represent a sub-class of bistable structures extensively studied, yet the relation between relevant boundary conditions and their bifurcation behaviors remains incompletely understood. Here we examine the bifurcation behavior of a buckled, elastic beam with both ends clamped in the absence of any external body force. Through a systematic investigation combining experiments, theory, and computational analysis, we identify that the beam can go through saddle–node bifurcation or pitchfork bifurcation (subcritical or supercritical) under asymmetric or symmetric boundary conditions, respectively. We construct the stability diagram in terms of the independent control parameters that can provide a precise prediction of the critical point upon bifurcation. Our results can not only provide powerful guidance on the design of fast switches, mechanical metamaterials, energy harvesters, or micro-electro-mechanical systems (MEMS) that exploit the bistability of elastic beams with clamped ends, but also have implications on a variety of biophysical phenomena and biomimetic structures.

A bistable vibration isolator with nonlinear electromagnetic shunt damping

Abstract This paper presents a bistable vibration isolator (BVI) with several ring permanent magnets (PMs) and utilizes nonlinear electromagnetic shunt damping (N-EMSD) to improve the vibration isolation performance of the BVI. The theoretical model of N-EMSD is established. The harmonic balance method (HBM) is employed to derive the transmissibility of the BVI with N-EMSD. The analytical, numerical and experimental efforts are performed to investigate the vibration isolation performance of the BVI with N-EMSD. The results demonstrate that when the BVI is in the interwell oscillation, two peaks appear in the transmissibility curve and the transmissibility could be smaller than 1 between the two peaks. With the increase of the negative resistance, the motion of the BVI changes from the aperiodic/chaotic interwell oscillation to intrawell oscillation, resulting in the increase of the isolation band and the improved vibration isolation performance. The effects of the nonlinear electromagnetic coupling coefficient and the negative resistance are also investigated. The BVI with N-EMSD provides a feasible approach to study the vibration isolation characteristic of bistable structures.

A Theory for the Design of Multi-Stable Morphing Structures

Multi-stable structures can provide desired reconfigurability and require relatively simple actuation. This paper considers general bar and plate structures connected by frictionless hinges that are to be made locally stable in a set of chosen target configurations by attaching extensional and rotational, linear-elastic springs to the structure. The unstressed lengths and angles of the springs, as well as their stiffnesses, are the unknown design parameters to be determined. A set of equilibrium and stability conditions to be satisfied in each of the target configurations of the structure are derived. Solutions of these equations provide specific values of the spring properties that correspond to local energy minima in all of the target configurations. The formulation is fully general and is applicable to structures of any complexity. A simple example is used to illustrate the design process for a bi-stable origami structure and a physical prototype is also presented.

Designing multi-stable structures with enhanced designability and deformability by introducing transition elements

Referring to the basic principle of bi-stable structures and the design of continuous multi-stable composite surfaces, a new method for designing multi-stable structures is proposed in this paper. The multi-stable plate is divided into deformation and transition elements. By introducing transition elements of which the stiffness is appropriately tailored, the geometric compatibility problem of multi-stable composite structure can be reduced. New multi-stable structures with different sizes, layers, one-direction splicing and two-direction splicing are manufactured. The experimental results demonstrate that these new multi-stable structures not only reduce the geometric compatibility but also have better designability of layers and sizes. The principle of generating geometric compatibility and influence of transition element stiffness on multi-stable structures are analyzed, as well as the relationship between the number of deformed elements and the number of deformation states. The shapes of the new multi-stable structure can be any value in theory. In the experiments, the maximum number of shapes reached 10. The deformability is also enhanced in comparison with other multi-stable structures.